By Arshad Mohammed COPENHAGEN, May 31 (Reuters) - U.S. Secretary of State Hillary Clinton on Thursday laid out arguments against armed intervention in Syria despite last week's massacre in the town of Houla. Speaking to Danish students, Clinton got tough questions on what might motivate the United States and other nations to take military action in Syria, where President Bashar al-Assad is battling a 14-month-old anti-government uprising. Friday's massacre of more than 100 civilians, many of them children, in Houla has triggered calls for the West to take more robust action in Syria, despite Russian and Chinese opposition. However, Clinton rehearsed U.S. arguments against armed intervention for now in contrast with Libya, where Western-led air strikes last year helped bring an end to Muammar Gaddafi's rule. Clinton said Syria had a more diverse society with greater ethnic divisions, no unified opposition, stronger air defenses and a much more capable military than Libya's. Above all, she stressed there was no international support because of Russian and Chinese opposition at the U.N. Security Council, where they have twice vetoed resolutions on Syria. "A lot of people are trying to figure out what could be an effective intervention that wouldn't cause more death and suffering," she said, arguing Syria's population density increased the odds of civilian casualties in any armed action. "We are thinking about all of this. There's all kinds of both civilian and humanitarian and military planning going on but the factors are just not there," she said. Clinton said she had not given up on the possibility of persuading Russia to support stronger action against the Assad government, saying she had made the case that the chances of a full-blown civil war were higher if the world failed to act. "The dangers we face are terrible," she said, saying the violence between government forces and pro-Assad militias against the opposition forces would turn into something much worse. "(That) could morph into a civil war in a country that would be riven by sectarian divides, which could then morph into a proxy war in the region because remember you have Iran deeply embedded in Syria," she said. "We know it could actually get much worse than it is. The Russians ... keep telling me they don't want to see a civil war and I have been telling them their policy is going to help contribute to a civil war," she said. Clinton did not describe any alternatives to United Nations-Arab League envoy Kofi Annan's efforts to try to stop the violence. "We are trying to keep pushing all the pieces to support Kofi Annan as an independent voice because the Syrians are not going to listen to us," she said. "They may listen, maybe, to the Russians, so we have been pushing them." (Editing by Janet Lawrence)